BRUSSELS (Reuters) - Amazon is talking to European Union antitrust regulators about settling a year-long investigation into its e-book deals with publishers without a fine, a person familiar with the matter said on Tuesday.

The move comes as Amazon is also under scrutiny over its tax deal with Luxembourg, which may result in the U.S. online retailer paying millions of euros in back taxes.

"Amazon is in talks to settle the e-book case but it is too early to say whether it will reach an agreement," said the source, who spoke on condition of anonymity.

Under the EU's settlement rules, the company would not face any fine or finding of wrongdoing if it can offer concessions to allay regulatory concerns.

European Commission spokesman Ricardo Cardoso declined to comment.

The EU competition watchdog opened an investigation into the case in June last year, saying Amazon's e-books contracts with publishers giving it terms as good as those for its rivals may make it difficult for other e-books distributors to compete.

The focus is on Amazon's e-books in English and German. The company is the biggest e-book distributor in Europe, while the market is growing rapidly.